Special Relativity

Consider a space rocket travelling towards a planet at speed c/2 with respect to an observer on the surface of the planet. The planet is 5.25 × 1011 km away from the rocket. The rocket has a rest length of 175 m. A probe is fired from the rocket towards the planet at a speed of 3c/5 with respect to the rocket. All motion occurs along the same straight line and c is the speed of light. (a) How fast in m s−1 is the probe moving with respect to the observer? (b) In the observer’s frame of reference, how much time does it take for the probe to travel from the rocket to the planet? (c) The observer is holding a clock. It displays 13:00:00. How much time will pass in the rocket’s frame of reference before the observer’s clock displays 14:00:00? (d) What is the length of the rocket in the probe’s frame of reference?